

A066389


Number of 2generated groups of order n: groups that have a generating set of size <=2, i.e., are cyclic or of the form <a,b>.


3



1, 1, 1, 2, 1, 2, 1, 4, 2, 2, 1, 5, 1, 2, 1, 9, 1, 4, 1, 5, 2, 2, 1, 13, 2, 2, 4, 4, 1, 4, 1, 20, 1, 2, 1, 12, 1, 2, 2, 12, 1, 6, 1, 4, 2, 2, 1, 35, 2, 4, 1, 5, 1, 10, 2, 11, 2, 2, 1, 13, 1, 2, 4, 54, 1, 4, 1, 5, 1, 4, 1, 37, 1, 2, 3, 4, 1, 6, 1, 35, 10, 2, 1
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OFFSET

1,4


LINKS

Eric M. Schmidt, Table of n, a(n) for n = 1..1023


PROG

(GAP)
IsTwoGenerated := function(G) if IsSolvableGroup(G) then return (Length(MinimalGeneratingSet(G)) <= 2); fi; return ForAny(List(ConjugacyClasses(G), Representative), g>ForAny(G, h>Size(Group(g, h)) = Size(G))); end; A066389 := function(n) local count, i; count := 0; for i in [1..NumberSmallGroups(n)] do if IsTwoGenerated(SmallGroup(n, i)) then count := count + 1; fi; od; return count; end; # Eric M. Schmidt, May 02 2013; shortened by Eric M. Schmidt, May 20 2013


CROSSREFS

Cf. A000001.
Sequence in context: A072342 A257089 A234541 * A077191 A050363 A166974
Adjacent sequences: A066386 A066387 A066388 * A066390 A066391 A066392


KEYWORD

nonn,nice


AUTHOR

Sharon Sela (sharonsela(AT)hotmail.com), Dec 23 2001


EXTENSIONS

More terms from Reiner Martin (reinermartin(AT)hotmail.com), Dec 29 2001
More terms from Eric M. Schmidt, May 02 2013


STATUS

approved



